Details

analyze409.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample149.0ms (0.7%)

Algorithm

1×

intervals

Results

36.0ms	128×	body	8192	exit
11.0ms	223×	body	128	valid
3.0ms	18×	body	512	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

568×	`neg-mul-1_binary64`
503×	`fma-def_binary64`
491×	`fma-neg_binary64`
484×	`div-sub_binary64`
416×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	152	21
4	338	18
5	1090	18
6	2902	18
7	3695	18
8	4706	18
9	4881	18

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

9.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.1b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	9.6b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	3.2b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series50.0ms (0.2%)

Counts

3 → 52

Calls

3 calls:

19.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
17.0ms	(/.f64 x (exp.f64 wj))
15.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

3 → 100

Calls

3 calls:

14.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
11.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
3.0ms	(/.f64 x (exp.f64 wj))

simplify112.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-neg_binary64`
444×	`fma-def_binary64`
331×	`distribute-rgt-in_binary64`
292×	`associate--l+_binary64`
278×	`distribute-lft-in_binary64`

Counts

152 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3154
1	583	3016
2	1604	2995
3	4798	2993
4	5298	2993

prune113.0ms (0.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	147	5	152
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	5	154

Error

0.1b

Counts

154 → 5

Alt Table

Status	Error	Program
	9.2b	(+.f64 wj (/.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (sqrt.f64 (+.f64 wj 1))) (sqrt.f64 (+.f64 wj 1))))
	5.3b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
	9.1b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
	36.3b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	0.9b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))

Compiler

Compiled 3257 to 1433 computations (56% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	0.0b	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
✓	0.1b	(*.f64 8/3 (pow.f64 wj 3))
✓	8.9b	(.f64 x (.f64 wj wj))

series60.0ms (0.3%)

Counts

4 → 72

Calls

4 calls:

28.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
20.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
8.0ms	(.f64 x (.f64 wj wj))
3.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`

Counts

4 → 96

Calls

4 calls:

5.0ms	(*.f64 8/3 (pow.f64 wj 3))
4.0ms	(.f64 x (.f64 wj wj))
3.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
0.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))

simplify123.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
521×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
479×	`fma-neg_binary64`
401×	`cancel-sign-sub-inv_binary64`

Counts

168 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3853
1	409	3376
2	1438	3085
3	4985	3004
4	5189	3004

prune216.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	173	5	178

Error

0.1b

Counts

178 → 5

Alt Table

Status	Error	Program
	9.1b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
▶	2.2b	(fma.f64 (.f64 (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
	36.3b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	30.9b	(.f64 (sqrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))) (sqrt.f64 (-.f64 (+.f64 (fma.f64 wj wj x) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))) (*.f64 (pow.f64 wj 3) (fma.f64 x 8/3 1)))))
	5.3b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))

Compiler

Compiled 6431 to 3515 computations (45.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(fma.f64 (.f64 (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))))
✓	0.6b	(cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)))
	8.9b	(.f64 x (.f64 wj wj))

series13.2s (58.5%)

Counts

3 → 72

Calls

3 calls:

12.9s

(fma.f64 (*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))

170.0ms

(*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))))

56.0ms

(cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`

Counts

3 → 65

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))))

1.0ms

(cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))

1.0ms

(fma.f64 (*.f64 (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))

simplify400.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

730×	`fma-def_binary64`
625×	`associate-/l*_binary64`
267×	`*-commutative_binary64`
164×	`+-commutative_binary64`
137×	`sub-neg_binary64`

Counts

137 → 233

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	733	13270
1	2610	11912
2	5099	11912

prune1.9s (8.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	469	2	471
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	470	6	476

Error

0.1b

Counts

476 → 6

Alt Table

Status	Error	Program
	9.1b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
✓	2.2b	(fma.f64 (.f64 (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
	58.2b	(fma.f64 (pow.f64 (pow.f64 wj 4) 1/3) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
	36.3b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	5.3b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
▶	0.9b	(-.f64 (fma.f64 5/2 (.f64 (.f64 wj wj) x) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 wj 2 (*.f64 (pow.f64 wj 3) 8/3)) (pow.f64 wj 3)))

Compiler

Compiled 41767 to 24728 computations (40.8% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 wj 2 (*.f64 (pow.f64 wj 3) 8/3)) (pow.f64 wj 3))
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 (.f64 wj wj) x) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 wj 2 (*.f64 (pow.f64 wj 3) 8/3)) (pow.f64 wj 3)))
✓	0.1b	(*.f64 (pow.f64 wj 3) 8/3)
✓	8.9b	(.f64 (.f64 wj wj) x)

series113.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

55.0ms	(-.f64 (fma.f64 5/2 (.f64 (.f64 wj wj) x) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 wj 2 (*.f64 (pow.f64 wj 3) 8/3)) (pow.f64 wj 3)))
35.0ms	(fma.f64 x (fma.f64 wj 2 (*.f64 (pow.f64 wj 3) 8/3)) (pow.f64 wj 3))
17.0ms	(.f64 (.f64 wj wj) x)
6.0ms	(*.f64 (pow.f64 wj 3) 8/3)

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-l_binary64`

Counts

4 → 96

Calls

4 calls:

11.0ms	(.f64 (.f64 wj wj) x)
9.0ms	(*.f64 (pow.f64 wj 3) 8/3)
7.0ms	(-.f64 (fma.f64 5/2 (.f64 (.f64 wj wj) x) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 wj 2 (*.f64 (pow.f64 wj 3) 8/3)) (pow.f64 wj 3)))
1.0ms	(fma.f64 x (fma.f64 wj 2 (*.f64 (pow.f64 wj 3) 8/3)) (pow.f64 wj 3))

simplify282.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
562×	`cancel-sign-sub-inv_binary64`
524×	`distribute-rgt-in_binary64`
340×	`exp-prod_binary64`
264×	`associate-l_binary64`

Counts

180 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3922
1	414	3473
2	1718	3204
3	4179	3099
4	4887	3099
5	4999	3099
6	4897	3099

prune375.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	160	6	166

Error

0.1b

Counts

166 → 6

Alt Table

Status	Error	Program
	9.1b	(+.f64 wj (/.f64 (-.f64 (*.f64 x (exp.f64 (neg.f64 wj))) wj) (+.f64 wj 1)))
✓	2.2b	(fma.f64 (.f64 (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)))) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
	58.2b	(fma.f64 (pow.f64 (pow.f64 wj 4) 1/3) (cbrt.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x))) (neg.f64 (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))))
	36.3b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	5.3b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
✓	0.9b	(-.f64 (fma.f64 5/2 (.f64 (.f64 wj wj) x) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 wj 2 (*.f64 (pow.f64 wj 3) 8/3)) (pow.f64 wj 3)))

Compiler

Compiled 5933 to 3255 computations (45.1% saved)

regimes800.0ms (3.6%)

Accuracy

Total 1.5b remaining (94.7%)

Threshold costs 0b (0%)

Counts

115 → 1

Compiler

Compiled 9978 to 6177 computations (38.1% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	20	31
2	25	31
3	27	31
4	28	31
5	28	31

end1.0ms (0%)

Compiler: Compiled 24 to 16 computations (33.3% saved)

sample4.0s (17.7%)

Algorithm

1×

intervals

Results

2.0s	3846×	body	8192	exit
590.0ms	6543×	body	128	valid
209.0ms	712×	body	512	valid
135.0ms	717×	body	256	valid
13.0ms	28×	body	1024	valid
9.0ms	87×	body	128	invalid
1.0ms	16×	body	128	overflowed

Compiler

Compiled 203 to 119 computations (41.4% saved)

Details

analyze409.0ms (1.8%)

sample149.0ms (0.7%)

simplify86.0ms (0.4%)

prune3.0ms (0%)

localize8.0ms (0%)

series50.0ms (0.2%)

rewrite35.0ms (0.2%)

simplify112.0ms (0.5%)

prune113.0ms (0.5%)

localize14.0ms (0.1%)

series60.0ms (0.3%)

rewrite18.0ms (0.1%)

simplify123.0ms (0.5%)

prune216.0ms (1%)

localize17.0ms (0.1%)

series13.2s (58.5%)

rewrite24.0ms (0.1%)

simplify400.0ms (1.8%)

prune1.9s (8.4%)

localize29.0ms (0.1%)

series113.0ms (0.5%)

rewrite40.0ms (0.2%)

simplify282.0ms (1.3%)

prune375.0ms (1.7%)

regimes800.0ms (3.6%)

simplify6.0ms (0%)

end1.0ms (0%)

sample4.0s (17.7%)

Profiling